I have a question

Why would global warming raise sea levels?

If my glass of ice water is full, and I let the ice melt, it doesn't over flow. This is because liquid water is more dense than ice. When water freezes it expands, so as ice melts it essentially contracts and takes up less volume. How would the melting of the polar ice caps and ice bergs raise sea levels?

I'm not a scientist, so I guess I'm missing something.

Maybe if all the polar bears drown it would raise sea levels a bit...